More and more integration

Calculus Level 4

\[\displaystyle \int_{-1}^{3} \left(\tan^{-1}\left(\dfrac{x}{x^{2}+1}\right) +\tan^{-1}\left(\dfrac{x^{2}+1}{x}\right) \right) \, dx \]

If the integral above can be expressed as \(m \pi\), find \(m\).

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